Infinite tetration for complex domain

Asked May 12 '20 at 06:14

Active May 12 '20 at 07:53

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$$f(z)=z^{z^{z^{.^{.}}}}$$ $$for\space z \space \in C\rightarrow C$$

Can we define the range of this function(convergence-divergence specifically) without taking help from fractals? I checked out some articles but I couldn't find any exhaustive theory for the complex domain. Any help will be appreciated :)

edited May 12 '20 at 07:53

asked May 12 '20 at 06:14

pjmathematician

The question is closely related to the Lambert W function, and noted in the article referenced there; I would follow the chain (I didn't yet). – metamorphy May 12 '20 at 06:53
Thanks for the reply, the 'article' you have referenced has some useful information for this question. Thanks again :) – pjmathematician May 12 '20 at 07:04

Infinite tetration for complex domain

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